Anyonic quantum computation from the Turaev-Viro invariant

Greg Kuperberg
University of California, Davis (UC Davis)

One of the approaches to feasible quantum computation is to look for physical materials that have anyonic topological phases. In this talk I will describe a kind of converse construction: Every unitary spherical category yields a lattice system with an anyonic topological phase via the Turaev-Viro invariant from the field of quantum topological invariants.
Some spherical categories are better than others for quantum computation, and the Turaev-Viro model is not necessarily the most economical or likely Hamiltonian, but it provides an across-the-board starting point. If the spherical category is modular, then the Turaev-Viro model splits into two topological phases with cancelling central charge.

The ideas that I will discuss mostly comes from an old, unpublished discussion with Alexei Kitaev.

Audio (MP3 File, Podcast Ready)

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